An MCMC Fitting Method for Triaxial Dark Matter Haloes

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the behaviour of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. The very strong assumptions about the symmetry of the lensing halo implied with circular or perturbative elliptical NFW models are not physically motivated and lead to incorrect parameter estimates with significantly underestimated error bars. We here introduce a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true uncertainty present in nature. Applying the MCMC triaxial fitting method to a population of NFW triaxial lenses drawn from the shape distribution of structure formation simulations, we find that including triaxiality cannot explain a population of massive, highly concentrated clusters within the framework of LCDM, but easily explains rare cases of apparently massive, highly concentrated, very efficient lensing clusters. Our MCMC triaxial NFW fitting method is easily expandable to include constraints from additional data types, and its application returns model parameters and errors that more accurately capture the true (and limited) extent of our knowledge of the structure of galaxy cluster lenses. (abridged)Comment: 18 pages, 15 figures. Updated to match published versio

3D time series analysis of cell shape using Laplacian approaches

Background: Fundamental cellular processes such as cell movement, division or food uptake critically depend on cells being able to change shape. Fast acquisition of three-dimensional image time series has now become possible, but we lack efficient tools for analysing shape deformations in order to understand the real three-dimensional nature of shape changes. Results: We present a framework for 3D+time cell shape analysis. The main contribution is three-fold: First, we develop a fast, automatic random walker method for cell segmentation. Second, a novel topology fixing method is proposed to fix segmented binary volumes without spherical topology. Third, we show that algorithms used for each individual step of the analysis pipeline (cell segmentation, topology fixing, spherical parameterization, and shape representation) are closely related to the Laplacian operator. The framework is applied to the shape analysis of neutrophil cells. Conclusions: The method we propose for cell segmentation is faster than the traditional random walker method or the level set method, and performs better on 3D time-series of neutrophil cells, which are comparatively noisy as stacks have to be acquired fast enough to account for cell motion. Our method for topology fixing outperforms the tools provided by SPHARM-MAT and SPHARM-PDM in terms of their successful fixing rates. The different tasks in the presented pipeline for 3D+time shape analysis of cells can be solved using Laplacian approaches, opening the possibility of eventually combining individual steps in order to speed up computations

Quantum gravity without vacuum dispersion

A generic prediction of quantum gravity is the vacuum dispersion of light, and hence that a photon's speed depends on its energy. We present further numerical evidence for a scale dependent speed of light in the causal dynamical triangulation (CDT) approach to quantum gravity. We show that the observed scale dependent speed of light in CDT can be accounted for by a scale dependent transformation of geodesic distance, whose specific functional form implies a discrete equidistant area spectrum. We make two non-trivial tests of the proposed scale transformation: a comparison with the leading order quantum correction to the gravitational potential and a comparison with the generalised uncertainty principle. In both cases, we obtain the same functional form. However, contrary to the widespread prediction of vacuum dispersion in quantum gravity, numerous experiments have now definitively ruled out linear vacuum dispersion beyond Planckian energy scales, and have now even constrained quadratic dispersion. Motivated by these experimental constraints we seek to reconcile quantum gravity with the absence of vacuum dispersion. We point out that given a scale dependent geodesic distance, a scale dependent time interval becomes essential to maintaining an invariant speed of light. We show how a particular scale dependent time interval allows a photon's speed to remain independent of its energy.Comment: Version published in International Journal of Modern Physics D. 13 pages, 3 figure

Final State of Gregory-Laflamme Instability

We describe the behavior of a perturbed 5-dimensional black string subject to the Gregory-Laflamme instability. We show that the horizon evolves in a self-similar manner, where at any moment in the late-time development of the instability the horizon can be described as a sequence of 3-dimensional spherical black holes of varying size, joined by black string segments of similar radius. As with the initial black string, each local string segment is itself unstable, and this fuels the self-similar cascade to (classically) arbitrarily small scales; in the process the horizon develops a fractal structure. In finite asymptotic time, the remaining string segments shrink to zero-size, yielding a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship. We further discuss how this behavior is related to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability, and estimate the fractal dimension of the horizon prior to formation of the naked singularity.Comment: 27 pages, 6 Figures. Chapter of the book `Black Holes in Higher Dimensions' to be published by Cambridge University Press (editor: G. Horowitz

Quantum Gravity from Causal Dynamical Triangulations: A Review

This topical review gives a comprehensive overview and assessment of recent results in Causal Dynamical Triangulations (CDT), a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory's phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications.Comment: 64 pages, 28 figure

Identikit 2: An Algorithm for Reconstructing Galactic Collisions

Using a combination of self-consistent and test-particle techniques, Identikit 1 provided a way to vary the initial geometry of a galactic collision and instantly visualize the outcome. Identikit 2 uses the same techniques to define a mapping from the current morphology and kinematics of a tidal encounter back to the initial conditions. By requiring that various regions along a tidal feature all originate from a single disc with a unique orientation, this mapping can be used to derive the initial collision geometry. In addition, Identikit 2 offers a robust way to measure how well a particular model reproduces the morphology and kinematics of a pair of interacting galaxies. A set of eight self-consistent simulations is used to demonstrate the algorithm's ability to search a ten-dimensional parameter space and find near-optimal matches; all eight systems are successfully reconstructed.Comment: 14 pages, 8 figures. Accepted for publication in MNRAS. To get a copy with high-resolution figures, use the web interface, or download the Identikit software, visit http://www.ifa.hawaii.edu/faculty/barnes/research/identikit